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I've tried doing some research, but I can't find a definitive answer. Do I need to replace all four tires on my 2005 X3? I've managed to get 77k miles out of my Pirelli Scorpions. I don't know how, I've never managed more than 30-40k from a tire in my life.

I`d replace them all together -- you will have significant differences between diameter of the old and new tires (driveline and electronics dont like that) and they will drive significantly differently. Why not do them all at once?

I`d replace them all together -- you will have significant differences between diameter of the old and new tires (driveline and electronics dont like that) and they will drive significantly differently. Why not do them all at once?

BMW shipped the Sport package X3s with different sized tires front and rear. Very likely for different width/profile tires to have different rolling circumference. So it would seem that replacing tires 2 at a time really would not be a problem if some X3s shipped new that way?

Very likely for different width/profile tires to have different rolling circumference.

Good point.

I haven't done the calculation, because I have never been interested in owning a vehicle with different size tires front to rear.
(Unless there was a real performance advantage, rather than looks.)

But I would imagine that BMW carefully selects the tire sizes in a "staggered" set-up so that the rolling circumference difference is very small.
Or tune the X-drive dynamics to compensate.

Given that a new tire has about 10mm. tread depth, I would think that the rolling circumference difference between old and new tires in a standard set-up is more of a concern.

But another factor is that the 2 pairs of tires (old and new) would also have very different road-holding ability on wet roads, for example.
X-drive would have to handle that on a constant basis - not really the intended purpose.

Tires changed on only one side would make me wonder about why those tires were replaced... typical scenario is accident damage.

It is interesting to note how Xdrive works here... you have full floating differentials front and rear. That means within reason there is no detrimental affect from different sized wheels side to side. A limited slip diff with slipper clutches would have issues with different sizes but that is not how BMW Xdrive is built.

In the middle there is a clutch but it is probably not engaged normally. The whole deal is driven off the ABS wheel sensors and computer. If one or more wheels turns at a rate significantly faster by some margin, then Xdrive makes corrections. This is where it would engage the center transfer case clutch. But the main thing it does is apply brakes on spinning wheels to limit wheel spin and thereby direct more engine torque into other wheels. Brakes do not care much about different wheel sizes.

Likewise since the sensor process is individual per wheel it matters not if some tires are better than others. The computer just adjusts based on conditions. So I would not worry too much about new tires on just one end versus the other.

Sport package came with 18" wheels and same size tires all around, someone correct me if I'm wrong but IIRC the staggered setup was an option.

I stand corrected... however the optional 19" wheel/tire package was an option and did have different sizes. I have the 19" wheel/tire package and forget it was not included with the standard sport package

I'm looking at an x3 with 4 pretty much new tires, however, it has 2 different brand on one side of the vehicle.

Maybe you need to be more specific.
You may be saying that 3 tires are the same make, and the 4th. is different,
or, as most people seem to be interpreting, it has 2 different brands (2 of one, 2 of the other),
and they have been split up side-to-side rather than the more expected front-to-back.

In either case, it suggests that someone has deemed it not important to have 4 matching tires.
I would infer from that the vehicle has not had the best of care in other ways, and pass on it.